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<span style="font-family: Arial; font-size: 14px; line-height: 24px; "><h2 class="first" style="margin-top: 0px; margin-right: 0px; margin-bottom: 20px; margin-left: 0px; padding-top: 0px; padding-right: 0px; padding-bottom: 6px; padding-left: 0px; font-size: 18px; font-weight: bold; line-height: 24px; border-bottom-width: 1px; border-bottom-style: solid; border-bottom-color: rgb(222, 223, 225); clear: none; ">&nbsp;&nbsp; &nbsp; &nbsp;鍘熺悊</h2>銆�銆�浠(1)錛?,h(0)=1錛宑atalan鏁版弧瓚抽�掑綊寮忥細<br>銆�銆�<strong>h(n)= h(0)*h(n-1)+h(1)*h(n-2) + ... + h(n-1)h(0) (鍏朵腑n&gt;=2)<br></strong>銆�銆�鍙︾被閫掑綊寮忥細<br>銆�銆�<strong>h(n)=((4*n-2)/(n+1))*h(n-1);<br></strong>銆�銆�璇ラ�掓帹鍏崇郴鐨勮В涓猴細<br>銆�銆�<strong>h(n)=C(2n,n)/(n+1) (n=1,2,3,...)</strong></span><div><span style="font-family: Arial; font-size: 14px; line-height: 24px; "><strong><br></strong>銆�銆�鍗＄壒鍏版暟鐨勫簲鐢?br>銆�銆�錛堝疄璐ㄤ笂閮芥槸閫掑綊絳夊紡鐨勫簲鐢級<br>銆�銆�<h3 style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 28px; padding-top: 0px; padding-right: 0px; padding-bottom: 0px; padding-left: 0px; font-size: 16px; font-family: Arial; line-height: 22px; "><a name="1_1" style="color: rgb(51, 102, 204); text-decoration: underline; "></a>鎷彿鍖栭棶棰?/h3><br>銆�銆�鐭╅樀閾句箻錛?P=a1&#215;a2&#215;a3&#215;&#8230;&#8230;&#215;an錛屼緷鎹箻娉曠粨鍚堝緥錛屼笉鏀瑰彉鍏墮『搴忥紝鍙敤鎷彿琛ㄧず鎴愬鐨勪箻縐紝璇曢棶鏈夊嚑縐嶆嫭鍙峰寲鐨勬柟妗堬紵(h(n)縐?<br><div   id="h3vzvrr"   class="spctrl" style="font-family: Arial; font-size: 14px; text-align: left; height: 10px; line-height: 10px; "></div>銆�銆�<h3 style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 28px; padding-top: 0px; padding-right: 0px; padding-bottom: 0px; padding-left: 0px; font-size: 16px; font-family: Arial; line-height: 22px; "><a name="1_2" style="color: rgb(51, 102, 204); text-decoration: underline; "></a>鍑烘爤嬈″簭闂</h3><br>銆�銆�涓�涓爤(鏃犵┓澶?鐨勮繘鏍堝簭鍒椾負1錛?錛?錛?#8230;錛宯錛屾湁澶氬皯涓笉鍚岀殑鍑烘爤搴忓垪?<br>銆�銆�鍒嗘瀽錛氬浜庢瘡涓�涓暟鏉ヨ錛屽繀欏昏繘鏍堜竴嬈°�佸嚭鏍堜竴嬈°�傛垜浠妸榪涙爤璁句負鐘舵�?#8216;1&#8217;錛屽嚭鏍堣涓虹姸鎬?#8216;0&#8217;銆俷涓暟鐨勬墍鏈夌姸鎬佸搴攏涓?鍜宯涓?緇勬垚鐨?n浣嶄簩榪涘埗鏁般�傜敱浜庣瓑寰呭叆鏍堢殑鎿嶄綔鏁版寜鐓?鈥鐨勯『搴忔帓鍒椼�佸叆鏍堢殑鎿嶄綔鏁癰澶т簬絳変簬鍑烘爤鐨勬搷浣滄暟a(a&#8804;b)錛屽洜姝よ緭鍑哄簭鍒楃殑鎬繪暟鐩?鐢卞乏鑰屽彸鎵弿鐢眓涓?鍜宯涓?緇勬垚鐨?n浣嶄簩榪涘埗鏁幫紝1鐨勭瘡璁℃暟涓嶅皬浜?鐨勭瘡璁℃暟鐨勬柟妗堢鏁般�?br>銆�銆�鍦?n浣嶄簩榪涘埗鏁頒腑濉叆n涓?鐨勬柟妗堟暟涓篶(2n,n),涓嶅～1鐨勫叾浣檔浣嶈嚜鍔ㄥ～0銆備粠涓噺鍘諱笉絎﹀悎瑕佹眰錛堢敱宸﹁�屽彸鎵弿錛?鐨勭瘡璁℃暟澶т簬1鐨勭瘡璁℃暟錛夌殑鏂規鏁板嵆涓烘墍姹傘�?br>銆�銆�涓嶇鍚堣姹傜殑鏁扮殑鐗瑰緛鏄敱宸﹁�屽彸鎵弿鏃訛紝蹇呯劧鍦ㄦ煇涓�濂囨暟浣?m+1浣嶄笂棣栧厛鍑虹幇m+1涓?鐨勭瘡璁℃暟鍜宮涓?鐨勭瘡璁℃暟錛屾鍚庣殑2(n-m)-1浣嶄笂鏈塶-m涓?1鍜宯-m-1涓?銆傚鑻ユ妸鍚庨潰榪?(n-m)-1浣嶄笂鐨?鍜?浜掓崲錛屼嬌涔嬫垚涓簄-m涓?鍜宯-m-1涓?錛岀粨鏋滃緱1涓敱n+1涓?鍜宯-1涓?緇勬垚鐨?n浣嶆暟錛屽嵆涓�涓笉鍚堣姹傜殑鏁板搴斾簬涓�涓敱n+1涓?鍜宯-1涓?緇勬垚鐨勬帓鍒椼�?br>銆�銆�鍙嶈繃鏉ワ紝浠諱綍涓�涓敱n+1涓?鍜宯-1涓?緇勬垚鐨?n浣嶄簩榪涘埗鏁幫紝鐢變簬0鐨勪釜鏁板2涓紝2n涓哄伓鏁幫紝鏁呭繀鍦ㄦ煇涓�涓鏁頒綅涓婂嚭鐜?鐨勭瘡璁℃暟瓚呰繃1鐨勭瘡璁℃暟銆傚悓鏍峰湪鍚庨潰閮ㄥ垎0鍜?浜掓崲錛屼嬌涔嬫垚涓虹敱n涓?鍜宯涓?緇勬垚鐨?n浣嶆暟錛屽嵆n+1涓?鍜宯-1涓?緇勬垚鐨?n浣嶆暟蹇呭搴斾竴涓笉絎﹀悎瑕佹眰鐨勬暟銆?br>銆�銆�鍥犺�屼笉鍚堣姹傜殑2n浣嶆暟涓巒錛?涓?錛宯錛?涓?緇勬垚鐨勬帓鍒椾竴涓�瀵瑰簲銆?br>銆�銆�鏄劇劧錛屼笉絎﹀悎瑕佹眰鐨勬柟妗堟暟涓篶(2n,n+1)銆傜敱姝ゅ緱鍑?杈撳嚭搴忓垪鐨勬�繪暟鐩?c(2n,n)-c(2n,n+1)=1/(n+1)*c(2n,n)銆?br>銆�銆�錛堣繖涓叕寮忕殑涓嬫爣鏄粠h(0)=1寮�濮嬬殑錛?br>銆�銆�綾諱技錛氭湁2n涓漢鎺掓垚涓�琛岃繘鍏ュ墽鍦恒�傚叆鍦鴻垂5鍏冦�傚叾涓彧鏈塶涓漢鏈変竴寮?鍏冮挒紲紝鍙﹀n浜哄彧鏈?0鍏冮挒紲紝鍓ч櫌鏃犲叾瀹冮挒紲紝闂湁澶氬皯涓柟娉曚嬌寰楀彧瑕佹湁10鍏冪殑浜轟拱紲紝鍞エ澶勫氨鏈?鍏冪殑閽炵エ鎵鵑浂錛?灝嗘寔5鍏冭�呭埌杈捐浣滃皢5鍏冨叆鏍堬紝鎸?0鍏冭�呭埌杈捐浣滀嬌鏍堜腑鏌?鍏冨嚭鏍?<br>銆�銆�<h3 style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 28px; padding-top: 0px; padding-right: 0px; padding-bottom: 0px; padding-left: 0px; font-size: 16px; font-family: Arial; line-height: 22px; "><a name="1_3" style="color: rgb(51, 102, 204); text-decoration: underline; "></a>鍑稿杈瑰艦鐨勪笁瑙掑墫鍒嗛棶棰?/h3><br>銆�銆�<br>銆�銆�姹傚皢涓�涓?a target="_blank"  style="color: rgb(51, 102, 204); text-decoration: underline; ">鍑稿杈瑰艦</a>鍖哄煙鍒嗘垚涓夎褰㈠尯鍩熺殑鏂規硶鏁般�?br>銆�銆�綾諱技錛氫竴浣嶅ぇ鍩庡競鐨勫緥甯堝湪濂逛綇鎵�浠ュ寳n涓鍖哄拰浠ヤ笢n涓鍖哄宸ヤ綔銆傛瘡澶╁ス璧?n涓鍖哄幓涓婄彮銆傚鏋滃ス浠庝笉絀胯秺錛堜絾鍙互紕板埌錛変粠瀹跺埌鍔炲叕瀹ょ殑瀵硅綰匡紝閭ｄ箞鏈夊灝戞潯鍙兘鐨勯亾璺紵<br>銆�銆�綾諱技錛氬湪鍦嗕笂閫夋嫨2n涓偣,灝嗚繖浜涚偣鎴愬榪炴帴璧鋒潵浣垮緱鎵�寰楀埌鐨刵鏉＄嚎孌典笉鐩鎬氦鐨勬柟娉曟暟?&nbsp;<br>銆�銆�<h3 style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 28px; padding-top: 0px; padding-right: 0px; padding-bottom: 0px; padding-left: 0px; font-size: 16px; font-family: Arial; line-height: 22px; "><a name="1_4" style="color: rgb(51, 102, 204); text-decoration: underline; "></a>鐢ㄧ粰瀹氳妭鐐圭粍鎴愪簩鍙夋爲鐨勯棶棰?/h3><br>銆�銆�<br>銆�銆�緇欏畾N涓妭鐐癸紝鑳芥瀯鎴愬灝戠涓嶅悓鐨?a target="_blank"  style="color: rgb(51, 102, 204); text-decoration: underline; ">浜屽弶鏍?/a>錛?br>銆�銆�錛堣兘鏋勬垚h錛圢錛変釜錛?/span>
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